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I am doing monte carlo simulations. In the first run the experiment is repeated e.g. 10000 times. The result looks like $x\pm y$, $y$ is the relative error. Next, I change a part of the experiment and run again, e.g. 10000 times and have the result $u \pm v$, $v$ the relative error.

It is possible that the difference between $x$ and $u$ is small and also there is the relative error. How can I assess this difference with respect to the relative errors?

Example:

  • First result: $91.6 \pm 9.84$
  • Second result: $95.12 \pm 12.33$

Is there a "real" difference in the results or is it just something within the errors?

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    $\begingroup$ Is $\pm y$ the error in the estimate of the mean, or do most/all of the $10000$ values fall in that interval? $\endgroup$
    – Henry
    Commented Oct 7, 2021 at 15:38

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A simple strategy is assume a normal distribution for your MC results. Please check if that applies to you, lot's of practical MC applications (at least my own experience) assume normal or log-normal distribution.

Now, you have your assumed distribution and all the individual recorded values. What's stopping you from something like t-test?

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  • $\begingroup$ Why assume any distribution at all when you almost always can obtain a very large sample? $\endgroup$
    – whuber ♦
    Commented Jul 16 at 2:04

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